We are designing a comparative analysis between an infected group and a healthy group but we are unsure as to how much patients we would need to have a meaningful comparison.
You need to define your hypothesis first, then do a power calculation based on what you're trying to compare.
Provided you have a clear, operational hypothesis, the amount of controls to carry out your study depends on your hypothesis -as well as the design you choose to test it. Cases and controls exist whenever you try to make statistical inference, be it about a therapy or interventional study, a case-control design or a diagnostic test assessment.
The comparison could be made with two sample sizes nx and ny of each population. For example, with the statistic difference of independent sample means. It is easy to obtain the variance of such statistic, and from here to obtain confidence intervals approximating the variance by its unbiased estimator, and using the Chebychev inequality.
As our friends mentioned, there are many factors involved to decide about your sample size. But to keep it simple, if I want to suggest you a number without knowing the details of your data. I would say at least you need 15 sample for each group so that the degree of freedom would be n1 + n2 - 2 = 28 in case of comparison. So that you can approximate it by normal distribution if you have information about your population parameters. So you need at least 15 number of sample for each group, Clearly, if you are able to have more number of sample based on your time and money, you can have more accurate comparison. Good luck :)
In order to avoid misleading information, it becomes necessary you let us know what do you want from de cases and their comparison with controls. If you already have them, one might assume you have in mind a case-control study. If you have studied each case and controls during a given time, you might be thinking about a cohorts study instead. In each instance the sample size calculation -provided you have a hypothesis- will be different.
Without knowing more about the system, I would guess 15 to 20 in each group. If you are lucky you will find that this is more than enough. If you are unlucky you will find that you should have used a larger sample size.
You need to consider several things:
1) Size of the population that you are trying to estimate.
2) Difference between treatment and control that you are willing to accept as non-significant even when the null hypothesis is false.
3) Variability in your sample.
4) Ethical considerations. This includes cruelty to test subjects and the generation of excessive hazardous waste.
Dear Medriano, I just want to add something to TA Ebert. Additional things to be considered are a) how much power you want; b) number of controls per case; c) is matched or un-matched case control study.
If your familiar with statistical package STATA, then there is command for calculating sample size for case control study. Good luck!
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